Edge, vertex and mixed fault diameters

Iztok Banič (Author), Rija Erveš (Author), Janez Žerovnik (Author)

Abstract

Let ▫${\mathcal{D}}^E_q(G)$▫ denote the maximum diameter among all subgraphs obtained by deleting ▫$q$▫ edges of ▫$G$▫. Let ▫${\mathcal{D}}^V_p(G)$▫ denote the maximum diameter among all subgraphs obtained by deleting ▫$p$▫ vertices of ▫$G$▫. We prove that ▫${\mathcal{D}}^E_a(G) \leqslant {\mathcal{D}}^V_a(G) + 1$▫ a for all meaningful ▫$a$▫. We also define mixed fault diameter ▫${\mathcal{D}}^M_{(p,q)}(G)$▫, where ▫$p$▫ vertices and ▫$q$▫ edges are deleted at the same time. We prove that for ▫$0 < l \leqslant a$▫, ▫${\mathcal{D}}^E_a(G) \leqslant {\mathcal{D}}^M_{(a-\ell,\ell)}(G) \leqslant {\mathcal{D}}^V_a(G) + 1$▫, and give some examples.

Keywords

vertex-connectivity;edge-connectivity;vertex fault diameter;edge fault diameter;mixed fault diameter;interconnection network;

Data

Language:	English
Year of publishing:	2009
Typology:	1.01 - Original Scientific Article
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	519.17
COBISS:	13396502
ISSN:	0196-8858
Views:	1127
Downloads:	98
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	teorija grafov;povezanost po točkah;povezanost po povezavah;povezavni okvarni premer;točkovni okvarni premer;mešani okvarni premer;povezovalna mreža;ne zaključna dela;Matematika;Teorija grafov;
URN:	URN:SI:UM:
Type (COBISS):	Article
Pages:	str. 231-238
Volume:	ǂVol. ǂ43
Issue:	ǂiss. ǂ3
Chronology:	2009
DOI:	10.1016/j.aam.2009.01.005
ID:	1472434